I feel like I have a pretty good way to talk about $\varepsilon$-$\delta$ to physics and engineering students (and possibly students in comp sci). But I am not very sure what I can do for chemistry and biology majors.
For instance, with physics / engineering, I feel like I can talk about designing an apparatus ($f$) whose output is some target value ($L$) with a given tolerance level ($\varepsilon$). How careful do they need to control their input ($\delta$)... etc etc
But when it comes to biology? Or chemistry? I am not sure what a good motivating analogy would be.
EDIT: Cross-posted on MathEducators.SE.